Isometric group actions on Hilbert spaces: structure of orbits
classification
🧮 math.GR
math.FA
keywords
groupactionfinitelygeneratedhilbertisometricorbitsactions
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Our main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.
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